As Carly Simon is showing me around her house on Martha’s Vineyard, Massachusetts, she mentions, matter-of-factly, that it is haunted. Guests in the spare bedroom always hear the same conversation, apparently, about a record deal.

At 64 she seems little changed from her Seventies heyday, a rangy blonde in a rah-rah skirt and knee-length snakeskin boots. And those teeth still have you shielding your eyes.

Indeed, such is the warmth of her wide and white smile, I resist the urge to point out that ghosts do not exist. Besides, even a sceptic like me cannot deny that there is a metaphorical presence in this house, the ghost of a man not yet dead.

I refer to James Taylor, her ex-husband and fellow singer-songwriter and guitarist. Fellow legend, too, for the couple were rock nobility who used to hang out with film stars and presidents, who topped the charts, who appeared together on the cover of Rolling Stone.

‘James built this house in 1969,’ she says, showing me old photographs of the building site. ‘It was just a cabin in the wood and we would sleep on a pull-out couch over there.’

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The house has expanded a great deal since then. It now has a recording studio, library, tennis court and a 45ft-tall watchtower that you reach by a nautical-style spiral staircase.

Today, with a dusting of snow on the surrounding fields, it feels cosy. There are candles everywhere, a log fire crackling in the grate and lentil soup cooking on the stove.

The room we are sitting in is dominated by a baby grand piano. There is a chessboard set up and an acoustic guitar propped against a rocking chair.

Her friends on the island have included Jackie Onassis and Bill Clinton. There are photographs of them but none of James Taylor that I can see.

‘James who?’ she says with a laugh.

Their marriage was one of the most glamorous, high-profile pairings of the Seventies, but it was pushed to the limits by his heroin addiction and infidelities.

When he picked up a venereal disease while on tour – ‘a road accident’, as the euphemism had it – he told her in this room.

Understandably, she didn’t take it well and swung at him with the nearest thing to hand, a guitar. When she calmed down she told him she had some news, too. She was pregnant.

They divorced in 1983 after 10 years and two children. He remarried, twice. She once, to a poet.

When I meet Ben, their 33-year-old son, I see James Taylor haunts his features, too. The resemblance is uncanny, even with his Mormon beard and beanie hat.

Ben Taylor lives in a cottage in the grounds here, but still sees a lot of his father. He is even closer to his mother, but he doesn’t exactly act as a go-between, because the two do not talk.

I get the impression Ben cannot even mention his mother’s name in his father’s company.

‘It is so important that Ben has a good relationship with his father,’ Simon says. ‘Given my druthers I would have a good relationship with him, too. But I don’t seem to have any druthers about me!’

Druthers?

‘Oh, is that an Americanism? It means given what I would rather have, I would rather have any relationship with James – be it frustrating, mediocre, whatever – than no relationship at all, than what we have now, which is a long empty alleyway of memories leading up to a big wall of silence.’

Blimey. You can tell she wrote her own lyrics, can’t you? Ben is a musician who has the same vocal style as his father.

‘Actually, I think the more Ben sings, the less like James he sounds,’ Simon says. ‘He is an interesting combination of the two of us. His voice box is more like mine but the way his tongue sits in his mouth, and the way he pronounces words, is just like James.’

Ben has performed on and co-produced his mother’s new album. It features a couple of new songs but is mostly new acoustic versions of her old songs, reinterpreted for a voice that is about half an octave lower than it used to be.

It includes Anticipation, Coming Around Again and – how could it not? – You’re So Vain, the original of which had Mick Jagger on backing vocals and was one of the biggest-selling singles of the Seventies.

If her ex-husband haunts this house, that song must haunt her. But she doesn’t seem to mind talking about it. Indeed, it was so cold when I arrived she poured shots of apricot cognac and sang, ‘Her cognac was apricot!’ which is a decent joke, if you recall the lyrics to You’re So Vain.

There is a website dedicated to that song which lists the dozens of times she has been asked by journalists over the years who, among her many former lovers, the song was written about. Cat Stevens? Kris Kristofferson? Mick Jagger?

The usual assumption is that it is Warren Beatty. The actor did, after all, ring her to thank her for the song, because he was so vain he thought it was about him.

At the time they had their affair, she has said, Beatty was still relatively undiscovered as a Don Juan. She felt she was one among thousands – ‘It hadn’t reached, you know, the populations of small countries.’

She has always refused to say who You’re So Vain is about, quite rightly arguing that people don’t really want the truth, they prefer the riddle. I tell her I am going to be the first journalist in almost 40 years not to ask her, because I’ve already worked out the answer. It’s about Willie Donaldson, isn’t it?

She laughs. ‘Yeah, that’s it. You’ve got it! Actually, I suppose it could have been about him, in that the time period would have been accurate, and a lot of the specifics in the story might have been embellished. I mean, the Leer jet could have been a Falcon. I don’t think Willie flew by Leer jet.’

Willie Donaldson was her least-likely conquest, or rather she was his. He was perhaps best known as the satirical author of The Henry Root Letters and the man who first staged Beyond the Fringe, but he was also a serial bankrupt, crack addict and pimp, one who ended up dying in a seedy London bedsit, his computer still logged onto a lesbian porn site.

But when they met he was a glamorous, Cambridge-educated playboy and impresario who had inherited a fortune and was going out with the actress Sarah Miles.

It was 1966. London was swinging. Carly Simon was 20. Donaldson described her as ‘the answer to any sane man’s prayers; funny, quick, erotic, extravagantly talented’.

Sadly for both of them, he wasn’t exactly a sane man. Eccentric would be a better word. They got engaged, then he dumped her.

‘I was madly in love with him,’ she says now. ‘And after he broke my heart I couldn’t regain my interest in men for four years. I kept trying to understand why I found him so exotic. It wasn’t just because he had an English accent.

'We met on July 8 and by July 20 he had moved out of his place with Sarah Miles and had moved in with me at Wilton Place. We went up to the Portobello Road to buy tea sets. It was gangbusters. Then the Dear John letter came on October 24.

'We started to communicate again once I was married to James and he wrote back saying: “There hasn’t been a day when I haven’t thought of you.” All this tenderness poured out of him, when I was at a safe distance!’

Is it possible that he was being kind when he left, because he knew how self-destructive he was?

‘I don’t think so. I think in retrospect it was a good thing that I didn’t marry Willie but it wasn’t that he was being kind. I think he knew his ways were too perverse for me, that I was too much of a prude.

'There was a story he told of my taking a bath then lying naked on the bed and saying: “What do you think?” That never happened. I have no idea why he felt the need to project that. He didn’t even have a bath tub!’

He used to call her Little Frog Footman. ‘I think it was from Cinderella. He did appreciate me. I don’t think I could have loved him as much as I did if he hadn’t brought out something that I really loved about myself. My boyfriend Richard, who you met earlier, he’s like that. He makes me feel so good about myself.’

Richard is a surgeon, a veteran of the first Gulf War, and a divorcee 10 years her junior.

He is handsome in an all-American, flinty-jawed way, and when we met he told me that, because his operations often take several hours, he likes to have music playing in the operating theatre – and yes, there is some Carly Simon on the playlist. And no, he’s not that kind of surgeon and that wasn’t how they met.

He is a leading specialist in laparoscopic surgery. Simon has had breast surgery, but it was reconstructive, following a mastectomy in the late Nineties. That must have concentrated her mind, I say, given her a stark intimation of her own mortality.

‘It sure did,’ she says. ‘One of the things about creativity is you can be in denial about these things. When I found out I had cancer, there were four hours in which I was pounding my head on the marble kitchen top saying, “I can’t believe it, I can’t believe it.” But then I felt as if this little army in uniform was flooding me. They had come to help me fight it. I felt really strong about it after that. It was one of the strongest periods of my life.’

There is a new biography of Warren Beatty, by Peter Biskind, which suggests that when he met Carly Simon in a bar and she told him about her breast cancer he looked uncomfortable and ran off. She has a copy of it on her bookshelf.

‘Oh God!’ she says, rocking back on her sofa. ‘I meant to hide that before you got here!’

The book quotes Beatty as saying he has slept with more than 12,000 women. That must make his ex-lovers feel pretty special!

‘You think? You know what? I’ve been flirting with the idea of writing an autobiography because I was talking to Mike Nichols about all these biographies coming out and he said I should never co-operate with them because look what they’ve done to Warren.

'That book is full of inaccuracies. I haven’t read it myself but Richard read out some passages, one of them saying I cut a swathe through the famous and notorious men of my generation. A swathe? I know exactly what I did every single day because I kept a daily diary from the age of seven until 1983 when I broke up with James.’

Was it therapeutic?

‘I needed much more therapy than that!’

Simon had a nervous breakdown in the early Sixties, one brought on by a wine allergy. She has been seeing therapists ever since and, to this day, suffers from a debilitating stage fright, which means she hardly ever performs in public.

‘When I’m feeling anxious or depressed, I do find it helps to reach for a pen and paper. There is something about writing things down, that hand-eye combination, that makes me feel calmer.

'Seeing things that are bothering you written down takes away their power. It gives you a perspective. Helps you contain them. The other day I was feeling so terrified and sad I had to pull the sheets over my head. I think Richard was a little shocked by my behaviour.’

Her parents seem to have been part of the problem. Her father, also called Richard, was a wealthy publisher, the Simon of Simon and Schuster. The young Carly grew up among the rich and famous of Manhattan. Not only Rodgers and Hammerstein but also George Gershwin were regular guests at the family home.

Her father died in 1960 when she was 15. ‘It was a difficult age. There was an emotional numbness surrounding his death for me that hasn’t been broken through yet. I had an even bigger reaction when I was 10 and I found out he had had his first heart attack. That demolished me. So freaked out.

'I would knock on wood 500 times every night thinking that would keep him from dying. Compulsive behaviour. The fact that he didn’t die the first night I did it meant I had to keep doing it. I was so scared. I eventually began knocking less, getting it down to 300, then 100 in the last year, then he died.’

There were unresolved issues. ‘I wanted him to live longer so that I could see him and my mother really love each other. I couldn't bear the thought that they didn’t have the perfect marriage, with the perfect house, and the perfect car and the perfect apple pie cooling on the window ledge.

'My mother fell in love with someone else, you see. And when my sisters told me when I was 12 that my parents didn’t love each other, that was when I started having serious anxiety attacks.’

Did that memory impinge upon her own marriage?

‘I think we do compensate by going off in the opposite direction. You can repeat the mistakes of your parents’ marriage or you can go out of your way not to repeat them.

'I heard Ben say the other day that he really doesn’t want to repeat what he saw in the relationship between myself and James. Yet those little repetitions sneak up on you from behind and there you are doing the same things your mother did to your father.’

She sounds like a hopeless romantic.

‘I am. As a child I used to read Gone with the Wind over and over again. I wanted to be Scarlett O’Hara. I never wanted to believe that it was possible that there could be infidelity. I never wanted to be believe that it was even possible for a man to look another way, even for a moment. My bubble of monogamy was pierced in a harsh way.’

Speaking of biographies, there was an excellent triple one which came out not long ago called Girls Like Us, about Joni Mitchell, Carole King and Carly Simon. It portrayed them as feminist icons, yet that is not how Simon saw herself at the time.

‘I wanted to be the little woman behind the man leading the academic life,’ she says. ‘I was too shy to be front of stage.

'The other day I came across a recording I made of a night at my apartment when I was living with Kris Kristofferson. Bob Dylan had been around earlier and we were all passing around the guitar. Whenever it came to my turn I would run into the kitchen and say I’d left the coffee on the stove or something. Shyness. Scared to perform.’

Shyness? Really? Wasn’t she shy and confident at the same time? Driving with her foot on the break and the accelerator?

‘Yes, but with me it goes from one extreme to the other like a pendulum, until I become the hum of the pendulum. I stole that line from Mike Nichols. If I say anything good, I’ve probably ripped it off. You’ve got to hear this recording. Can I play it for you?’

She goes upstairs, returns with a MacBook Pro and finds the sound file. Kris Kristofferson sounds drunk when he is talking but when he is playing his guitar and singing he sounds pretty good.

Was it only the guitar they were passing around?

‘As I recall, it was more about booze that night. I did used to smoke grass though. There was a time for about two years when I would roll myself a joint every morning when I woke up.’

Not good.

‘Why?’

Ending the day with a joint, maybe. But starting it? Surely that’s a slippery slope.

‘But you get used to it. I guess I was stoned as much of the waking hour as I wasn’t stoned. I stopped it all very suddenly when I was pregnant with Sally.’

Simon began her career as part of a double act with her sister Lucy. They were called the Simon Sisters and on the cabaret circuit they opened for Woody Allen, among others.

They split up when Lucy married a psychiatrist and had a child. They still sometimes duet on the phone but it must have been hard for Lucy to watch as her sister’s solo career took off?

‘I guess it was but if she felt that, she had the good grace not to show it. She was never going to say to me, “Damn you and your number one singles”. That said, my family were all pretty piqued around the time I married James. That seemed too much for us to all of a sudden become like this royal couple. Yet it was never discussed. I still feel a little guilty about it.’

Because?

‘Because I wasn’t the one who wanted fame, but got it anyway.’

Famous people had always surrounded her, though. Is that why the Clintons and Jackie Onassis found it easy to be in her company? Because she wasn’t star struck?

‘Probably. I remember with Jackie especially…’ She trails off.

‘Sorry, but she was Jackie to me. To try and be coy about it would be even more obnoxious than sounding as if I was name-dropping. I used to take great pleasure in being relaxed in front of her and think she appreciated that because she always seemed relaxed with me.

'I think a lot of the people in her life were emotionally uptight and not willing to share. We had a similar sense of humour and were attracted to a lot of the same people. We loved each other and I remember one of the first times we had lunch together I was really nervous because she was half an hour late.

'She had been stuck in the elevator but she turned up as calm as anything and I was the one who was hyperventilating. I had to take a Valium washed down with gin. She thought this was funny and told me I was like a thoroughbred racehorse. High strung. Which is true.’

It is nearly dusk and Richard comes in from outside. He has been clearing wood and now has a bonfire going. Simon suggests we all go out and roast marshmallows on it. She puts on a black velvet frock-coat with a furry collar and, carrying a packet of marshmallows in one hand, picks up a guitar in the other.

Well, it is a campfire and she is Carly Simon. Somehow she manages to strum while wearing long, white silk evening gloves. A thoroughbred racehorse, indeed.